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Section 3.1
Relations and Functions
Objective 1:
Understanding the Definitions of Relations and Functions
Definition
Relation
A
relation
is a correspondence between two sets
A
and
B
such that each element of set
A
corresponds to one or more elements of set
B.
Set
A
is called the
domain
of the relation and set
B
is called the
range
of the relation.
Definition
Function
A
function
is a relation such that for each element in the domain, there corresponds
exactly
one and only one
element in the range.
In other words, a function is a welldefined relation.
The elements of the domain and range are typically listed in ascending order
when using set
notation.
Objective 2:
Determine if Equations Represent Functions
To determine if an equation represents a function, we must show that for any value of
in the domain, there is
exactly one corresponding value in the range.
Objective 3:
Using Function Notation; Evaluating Functions
When an equation is explicitly solved for
y
, we say that “
y
is a function of
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 Spring '09
 moshe
 Algebra, Sets

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